|
Search: id:A072873
|
|
|
| A072873 |
|
Numbers n such that sum( e(i)/p(i) ) is an integer, where the prime factorization of n is prod ( p(i)^e(i) ). |
|
+0
5
|
|
| 1, 4, 16, 27, 64, 108, 256, 432, 729, 1024, 1728, 2916, 3125, 4096, 6912, 11664, 12500, 16384, 19683, 27648, 46656, 50000, 65536, 78732, 84375, 110592, 186624, 200000, 262144, 314928, 337500, 442368, 531441, 746496, 800000, 823543
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
Also, numbers n such that n divides n', the arithmetic derivative of n. As shown by Ufnarovski and Ahlander, all terms in this sequence have the form prod_{k=1..r} (pk^pk)^ek, where the pk are primes. The quotient n'/n equals sum_{k=1..r} ek. - T. D. Noe (noe(AT)sspectra.com), Jan 04 2006
|
|
REFERENCES
|
See A003415.
|
|
EXAMPLE
|
108 is in the sequence because 108 = 2^2*3^3 and 2/2+3/3 = 2 is an integer
|
|
MAPLE
|
P:=proc(p) local a, b, m, n, i, ok, t1, t2, t3; a:=0; for n from 1 by 1 to p do b:=1000000000039; ok:=0; if n<=1 then a:=0; ok:=1; fi; if isprime(n) then a:=1; ok:=1; fi; if ok=0 then t1:=ifactor(b*n); m:=nops(t1); t2:=0; for i from 1 to m do t3:=op(i, t1); if nops(t3)=1 then t2:=t2+1/op(t3); else t2:=t2+op(2, t3)/op(op(1, t3)); fi; od; t2:=t2-1/b; a:=n*t2; fi; if (a mod n)=0 then print(n); fi; od; end: P(1000000); [From Paolo P. Lava (ppl(AT)spl.at), Nov 13 2009]
|
|
CROSSREFS
|
Sequence in context: A046346 A134330 A097764 this_sequence A072653 A008478 A111260
Adjacent sequences: A072870 A072871 A072872 this_sequence A072874 A072875 A072876
|
|
KEYWORD
|
nonn,new
|
|
AUTHOR
|
Benoit Cloitre (benoit7848c(AT)orange.fr), Jul 28 2002
|
|
EXTENSIONS
|
More terms from T. D. Noe (noe(AT)sspectra.com), Jan 04 2006
|
|
|
Search completed in 0.002 seconds
|
